On Oct 3, 2011, at 9:28 AM, Stephen A. Lawrence wrote:
In general, it's only after things dip well below 90% that the "naive formula" starts going seriously wrong.
Good point, though I suppose I should have more fully expressed what I meant.
I changed the referenced text to read: "For example, if the probability of a catastrophe when drinking and driving once is 1/1000 = .001, then the probability of a catastrophe in 600 such events is 1-.999^600 = 0.45, or about 45%. Of course the probability of a catastrophic event is much larger if the drinking is very heavy, perhaps 0.1. The probability of a catastrophe in 20 such events is 1-0.9^20 = 0.878, or about 88%. Each event is independent, yet the combined effect of repeating events has a dependent nature. This is sometimes called the Russian roulette effect."
I think part of the problem the typical person, who has little or no knowledge of probability at all, faces is a lack of appreciation for the cumulative effect of repeated risk. This was more my jist than the "naive formula" error. Perhaps this stems from an intuitive Bayesian model of reality. If a person does not or can not update his own mental Bayesian model from the experiences of others then he tends to expect no possibility of catastrophe for himself, until it happens. This is a gross over simplification but it is my general impression. It is a different situation for an experienced gambler, but there are of course a number of other logical fallacies and biases a gambler has to overcome, as I pointed out in my "A Perspective on Gambling" article:
http://mtaonline.net/~hheffner/Gambling.pdf Best regards, Horace Heffner http://www.mtaonline.net/~hheffner/
